10-15 planets is just big enough that rushing might not be possible. If you have a fairly clear path to the guy, you can hit him while he is still in the economic stage with Assailants...otherwise, you have to get carriers with fighters to counter LRM spam and try to get your own econ going. If he goes Kodiaks and doesn't have fighters of his own, you can switch to bombers.
Vasari econ is about fast expansion with the Evacuator and grabbing the neutral extractors on the map if there are any. Do hit and runs with your carriers, but otherwise, try to make him fight on your terms near your repair bays. Mid game is hard for Vasari because the ships are so expensive vs the cheap TEC spam. Just keep an eye on the other guy and make sure you have counter units to whatever he is building, get your phase gates up, and use them to raid and rapidly reinforce.
The main thing to remember is if you can't kill the TEC guy fairly quickly, you will probably need your own Econ/tradeports to survive, so expand, dig in, and get a few tradeports of your own up.